Electrowetting can be described by the Lippmann equation:
                              γ          SL                =                              γ            SL            0                    -                                    1              2                        ⁢                          CV              2                                                          (        1        )            where γSL0 is the voltage-free solid-liquid interface energy, C is the capacitance between the drop and surface, and V is the voltage applied. In the case of electrowetting on dielectrics (EWOD), the capacitance C can be expressed by:
                              C          =                                                    ɛ                0                            ⁢                              ɛ                r                            ⁢              A                        d                          ,                            (        2        )            where ∈0 is the permittivity in vacuum, ∈r is the dielectric constant, A is the drop's contact area and d is the thickness of the dielectric layer. Since the contact angle can be expressed according to Young equation:
                                          cos            ⁢                                                  ⁢            θ                    =                                                    γ                S                            -                              γ                SL                                                    γ              L                                      ,                            (        3        )            
Combining equation (1)-(3), we get:
                    θ        =                  arc          ⁢                                          ⁢                                    cos              (                                                                    γ                    S                                    -                                      γ                    SL                    0                                    +                                                                                                              ɛ                          0                                                ⁢                                                  ɛ                          r                                                ⁢                        A                                                                    2                        ⁢                        d                                                              ⁢                                          V                      2                                                                                        γ                  L                                            )                        .                                              (        4        )            
Eq. (4) suggests that there are two parallel approaches to reduce the driving voltage. One way is to increase the capacitance, either by decreasing the dielectric layer thickness or employing a coating with high dielectric constant; the other way is to minimize the interfacial energies of the solid (γS−γSL0) and the liquid (γL), usually through using an immiscible oil bath. The first approach can reduce the driving voltage down to ˜15V by employing a thin fluoropolymer coating. If combined with the oil bath approach, electrowetting can be achieved at less than 3V, at the price of incompatibility with digital micro-fluidics applications.
This document describes a low voltage electrowetting device incorporating an ionic liquid dielectric layer of ultrahigh capacitance. Such a device is capable of electrowetting effects using driving voltages of just 70 mV and 5 V in AC and DC modes of operation. Further, such a device is compatible with digital micro-fluidics applications.